凍結面に吸排水を伴う定常厳密解とその応用
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概要
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This paper gives an exact solution of heat transfer equations in freezing soil with constant freezing speed accompanying uniform suction flow to the freezing front, as a boundary value problem. Temperatures in frozen and unfrozen soil, θ<SUB>1</SUB> and θ<SUB>2</SUB> respectively, are :<BR>θ<SUB>1</SUB>=κ<SUB>1</SUB>/k<SUB>1</SUB> (k<SUB>2</SUB>/κ<SUB>2</SUB><I>U</I>+ν/<I>U</I>+υ<SUB>h</SUB>θ<SUB>∞</SUB>+γ<SUB>w</SUB><I>L</I><SUB>w</SUB>u<SUB>f</SUB><I>U</I>+υ<SUB>w</SUB>/<I>U</I>+υ<SUB>h</SUB>) {1-exp (-<I>U</I>+υ<SUB>h</SUB>/κ<SUB>1</SUB>ζ)} for ζ<0 and<BR>θ<SUB>2</SUB>=θ<SUB>∞</SUB> {1-exp (-<I>U</I>+ν/κ<SUB>2</SUB>ζ)}, for ζ>0, <BR>where, ζis variable of moving coordinate system with the same speed of the freezing front (at the freezing front ζ=0), <I>U</I> the constant advancing speed of freezing front, υ<SUB>w</SUB>the constant suction speed of water from unfrozen soil to the freezing front, υ<SUB>h</SUB> the heaving speed of frozen soil, <BR>υ<SUB>h</SUB> = (1+Γ) (υ<SUB>w</SUB>+n<SUB>f</SUB>1/1+Γ<I>U</I>), <BR>where Γ is the ratio of volume increase of water when freezing (≅ 0.09), n<SUB>f</SUB> the volumetric content of freewater in the vicinity of the freezing front, κ<SUB>1</SUB>, κ<SUB>2</SUB> the thermal diffusivity of frozen and unfrozen soil respectively, k<SUB>1</SUB>, k<SUB>2</SUB> the thermal conductivity of frozen and unfrozen soil respectively; νthe parameter defined as<BR>ν=<I>C</I><SUB>w</SUB>γ<SUB>w</SUB>/<I>C</I><SUB>s</SUB>γ<SUB>s</SUB>υ<SUB>w</SUB><BR>where γ<SUB>w</SUB> the weight of unit volume of pore water, γ<SUB>s</SUB> the weight of unit volume of unfrozen soil, <I>C</I><SUB>w</SUB> the specific heat of pore water, and <I>C</I><SUB>s</SUB> the specific heat of unfrozen soil; <I>L</I><SUB>w</SUB> the latent heat of pore water in freezing, and θ<SUB>∞</SUB> the initial temperature of unfrozen soil.<BR>In these equations the value of suction speed of pore water υ<SUB>w</SUB> can be taken independently to the freezing speed <I>U</I>. However authors have shown previously (Takashi <I>et al</I>., 1974) that υ<SUB>w</SUB> is a function of <I>U</I>;<BR>υ<SUB>w</SUB>=<I>U</I>/1+Γσ<SUB>0</SUB>/σ (1+√<I>U</I><SUB>0</SUB>/<I>U</I>) -n<SUB>f</SUB>Γ/1+Γ<I>U</I>, <BR>where, σ the effective stress in soil under freezing, σ<SUB>0</SUB>, <I>U</I><SUB>0</SUB> the characteristic constants of soil.<BR>Therefore if the last equation is applicable to all kind of soils it would be said that the present problem was solved completely.
- 社団法人 日本雪氷学会の論文
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